The Book of the Week is a signed copy of the first edition of A Game of Thrones by George R.R. Martin. A Game of Thrones is the first book in the Song of Ice and Fire fantasy series, the fourth volume of which - last week's Book of the Week, A Feast for Crows - hit #1 on the New York Times bestseller list a week ago.
One of the peculiarities of collecting books is that authors' most successful books are often not the ones in which collectors are interested. Because A Feast for Crows is selling so well, it will never be a rare book, for there are too many copies of it in circulation. However, the success of the later books in the Song of Ice and Fire series has caused the original edition of A Game of Thrones, which did not sell very well when released, to become a highly prized collector's item, only nine years after it was published.
Incidentally, the cover depicts the throne of the imaginary kingdom various characters vie to control in A Song of Ice and Fire. Called the "Iron Throne," it was constructed by an earlier ruler out of the swords of his vanquished enemies. This makes it a rather hazardous and uncomfortable place to sit, a nice visual representation of the Shakespeare line, "Uneasy lies the head that wears a crown."